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arXiv · 1612.08982

Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects

Harbir Antil·Enrique Otarola·Abner J. Salgado
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Abstract

We consider an identification problem, where the state $u$ is governed by a fractional elliptic equation and the unknown variable corresponds to the order $s \in (0,1)$ of the underlying operator. We study the existence of an optimal pair $(\bar s, \bar u)$ and provide sufficient conditions for its local uniqueness. We develop semi-discrete and fully discrete algorithms to approximate the solutions to our identification problem and provide a convergence analysis. We present numerical illustrations that confirm and extend our theory.

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Harbir Antil, Enrique Otarola, Abner J. Salgado. 2016-12-28. Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects. https://arxiv.org/abs/1612.08982

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